Geo-potential methods have been primarily used to delineate the sub-surface configuration and determine the magmatic and tectonic activity of the earth. These measurements are forerunners to other geophysical methods to provide the first hand information to the constituents of the earth.
Preparation of contour maps is one of the important steps in the analysis of geophysical data for interpretation of 3-dimensional causative sources. Before the advent of computers laborious hand contouring is the only way. With the invention of computers these procedures became very fast in main frame computers and through personal computers. As a result, the time and labor involved in scientific computation has drastically cut down.
The U.S. Geological Survey (USGS) began developing software for processing Potential-Field geophysical data shortly after pioneering airborne magnetic surveys in the late 1940's. Originally scientists wrote their own programmes, following their own methodology. Initially all these programs were developed in different versions and formats. In 1971 a standardized binary format for grid, line and point data was established allowing free sharing of programs developed by various scientists. The result was a pool of constantly evolving software representing a combined effort of all scientific community. Substantially costs were involved in these research and developments to make these programs error free.
Recognizing this software system to be a potentially valuable resource USGS provided the system for implementation on micro-computers which are widely available world over and provide a good medium for training and education.
Presently more than 270 programs, subprograms and subroutines are available in USGS-PF package. Although most of these programs have been in use for quite some time on various types of computers, some are new and a few of the programs have been much exercised and tested on personal computers.
MEGAPLUG subroutine replaces no-data (dval) values in a grid with values interpolated using the minimum curvature routines from program MINC. The blank areas to be filled may be of any size and shape as the program treats the existing grid data as random points. The default mode fills the entire grid and an optional mode trims the filled areas back to hulls surrounding contiguous data defined by the original grid (to fill holes within an irregular data region and leave the area outside the data region unfilled). Since the program contains the entire grid in memory, the size is limited to 50,000 grid points, but this could probably be increased somewhat.
Using MINC and running MEGAPLUG programs we can generate a grid file which gives better plots with less artifacts, but the quality of plots generated by USGS-PF package plot programs are poor in quality and can not be plotted to desired size and are basically being machine specific.
Presently many contouring and plotting packages are available in the market, ‘Surfer’ package developed by GOLDEN SOFTWARE, INC. USA is widely used by geo-scientists. It is a very useful package and can be used for creating XYZ data files, gridding and plotting and making various types of contour maps with lot of options.
Surfer generates grids by using various method of gridding such as inverse distance, krigging, polynomial regression, radial, minimum curvature, etc. Each method can result in different representation of data. It is advantageous to test each method with a typical data to determine the gridding method that provides the most satisfying interpretation of data.
The inverse distance to a power gridding method is weighted average interpolator and can be either an exact or a smoothing interpolator. With inverse distance the data points are weighted during interpolation such that the influence of one data point related to other decline with distance from the grid note. Weighting is assigned to data points through the use of a weighting power that controls how the weighting factors drop off as distance from the grid note increases. The greater the weighting power, the less effect points for from the grid note have during interpolation. As the power increases the grid node value approaches the value of nearest data point. For a smaller value of the weighting factor the weights are more evenly distributed among the neighboring data points. When calculating a grid node the weights assigned to the data points are fractions and the sum of the weights equal to 1.0. When an observation is coincident with the grid node the observation is given a weight 1.0, and all other observation are given a weight 0.0 One of the characteristic of inverse distance is the generation of Bull's eyes surrounding the position of observation within the gridded area. Smoothing parameters can be assigned during inverse distance to reduce the Bull's eye effect by smoothing the interpolated grid. Inverse distance is a very fast method gridding useful for smaller number of data points.
Kriging is a geo-statistical gridding method, which has been found to be very useful in many fields. Kriging attempts to express trend that are suggested in the data, so that higher valued points are connected along a ridge, rather than isolated by Bull's eye type of contours. There are several factors that are interpolated in the Kriging method: the Variogram model, the drift type and the nugget effect.
Polynomial regression is used to define large scale trends and patterns in your data.
There are several options to define the trend surface. Polynomial regression is not really a interpolator because it does not attempt to predict unknown z values.
Radial basis functions are a diverse group of data interpolation methods, in terms of ability to fit the data and to produce a smooth surface. The multi-quadratic method is considered to be the best method. All of the radial basis function methods are exact interpolators, so they make an attempt to honor the data. A smoothing factor can be introduced to all the methods in an attempt to produce a smooth surface.
Minimum curvature is widely used in earth sciences. The interpolated surface generated by the minimum curvature is analogous to a thin linearly elastic plate passing through each of the data values with a minimum of bending. Minimum curvature generates the smoothest possible surface while attempting to honor the data as closely as possible. Minimum curvature is not an exact interpolator, which means that the data is not always honored exactly.
Minimum curvature produces a grid by repeated applying an equation over the grid in attempt to smoothen the grid. Each pass over the grid is counted as one iteration. The grid node values are recalculated until successive changes in the values are less than the maximum residuals values or the maximum number of iterations is reached.
Minimum Curvature method of gridding of scattered data is one among various programs and subroutines provided by USGS-PF package. This program developed by Mike Webring, generates a 2-dimensional grid, equally incremented in x and y, from randomly placed data points. The minimum curvature algorithm produces a smooth grid by iteratively solving a set of difference equations, which minimize the total 2nd horizontal derivative and attempt to honor input data. (Briggs, 1974)
Geophysical measurements have contribution from different interfaces, which have lateral and vertical dimensions. Deviation from standard earth models is interpreted in terms of geological, physical/chemical changes in the sub-surface earth. Extensive software packages have been developed to interpret for the density and magnetic property heterogeneities in the earth in terms three dimension causative sources. However, most of the softwares have the compatibility problems, when implemented on different personal computers. The potential field contour maps generated by USGS professional software are not compatible to most of the personal computers. Apart from this the contour plots are not smooth to have meaningful interpretation in terms of the causative source.